The versatile Greek international has been linked with a move to the Olimpico and become the first signing under the club's new American ownership
The 25-year-old, who can play in a variety of positions, has been plying his trade for the Greek champions since 2007, appearing over 100 times for Ernesto Valverde's outfit.
His consistency over several years for both club and country has ignited the interest of Roma, as the Giallorossi are on the lookout for reinforcements at the back, and have identified the Greek utility man as a signing that will bolster their defence.
Roma, who have also been contacted in recent days by Olympiakos for playmaker David Pizarro, would have no problem in negotiating a transfer fee, after being bought by wealthy American-Italian businessman Thomas DiBenedetto, and Torosidis' market valuation is reported to be around €8 million.
However, he has a contract that will not expire until 2015, so the Lupi will likely have to pay top dollar to land the player.
Olympiakos had another successful season, regaining their Greek Super League title, while Roma had contrasting fortunes, finishing sixth in Serie A.